Let mu be a measure on a measure space (X, Lambda) with values in R-n and f be the density of mu with respect to its total variation. We show that the range R(mu)= {mu(E) : E is an element of Lambda} of mu is strictly convex if and only if the determinant det[f(x(1)),..,f(x(n))] is nonzero a.e, on X-n. We apply the result to a class of measeres containing those that are generated by Chebyshev systems. (C) 1999 Academic Press.

The vector measures whose range is strictly convex

MARICONDA, CARLO
1999

Abstract

Let mu be a measure on a measure space (X, Lambda) with values in R-n and f be the density of mu with respect to its total variation. We show that the range R(mu)= {mu(E) : E is an element of Lambda} of mu is strictly convex if and only if the determinant det[f(x(1)),..,f(x(n))] is nonzero a.e, on X-n. We apply the result to a class of measeres containing those that are generated by Chebyshev systems. (C) 1999 Academic Press.
File in questo prodotto:
File Dimensione Formato  
99vectormeasstrconv.pdf

accesso aperto

Tipologia: Published (publisher's version)
Licenza: Accesso libero
Dimensione 157.69 kB
Formato Adobe PDF
157.69 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/2486783
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
  • OpenAlex ND
social impact